Enhancing accuracy of fast high-resolution x-ray diffractometry

ABSTRACT

A method for analysis includes directing a converging beam of X-rays toward a surface of a sample and sensing the X-rays that are diffracted from the sample while resolving the sensed X-rays as a function of angle so as to generate a diffraction spectrum of the sample. The diffraction spectrum is corrected to compensate for a non-uniform property of the converging beam.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional PatentApplication 61/363,653, filed Jul. 13, 2010, which is incorporatedherein by reference.

FIELD OF THE INVENTION

The present invention relates generally to X-ray analysis, andspecifically to measurements of high-resolution X-ray diffraction.

BACKGROUND OF THE INVENTION

X-ray diffractometry (XRD) is a well-known technique for studying thecrystalline structure of matter. In XRD, a sample is irradiated by amonochromatic X-ray beam, and the locations and intensities of thediffraction peaks are measured. The characteristic diffraction anglesand the intensity of the diffracted radiation depend on the latticeplanes of the sample under study and the atoms that make up thecrystalline material. For a given wavelength λ and lattice plane spacingd, diffraction peaks will be observed when the X-ray beam is incident ona lattice plane at angles θ that satisfy the Bragg condition: λ=2d sinθ_(B). The angle θ_(B) that satisfies the Bragg condition is known asthe Bragg angle. Distortions in the lattice planes due to stress, solidsolution, defects or other effects lead to observable changes in the XRDspectrum.

XRD has been used, inter alia, for measuring characteristics ofcrystalline layers produced on semiconductor wafers. For example, U.S.Pat. No. 7,120,228, whose disclosure is incorporated herein byreference, describes a combined X-ray reflectometer and diffractometer.The described apparatus includes a radiation source, which is adapted todirect a converging beam of X-rays toward a surface of the sample. Atleast one detector array is arranged to sense the X-rays scattered fromthe sample as a function of elevation angle over a range of elevationangles simultaneously. In one configuration, the detector array sensesthe X-rays that are diffracted from the surface in a vicinity of a Braggangle of the sample. A signal processor processes the output signalsfrom the detector array so as to determine a characteristic of thesurface layer of the sample.

Other systems for XRD measurement are described, for example, in U.S.Pat. Nos. 7,076,024 and 7,551,719, whose disclosures are alsoincorporated herein by reference.

SUMMARY

Embodiments of the present invention that are described hereinbelowprovide techniques that may be used to enhance the accuracy of X-rayscattering measurements, and particularly of fast, high-resolution XRD(HRXRD).

There is therefore provided, in accordance with an embodiment of thepresent invention, a method for analysis, which includes directing aconverging beam of X-rays toward a surface of a sample and sensing theX-rays that are diffracted from the sample while resolving the sensedX-rays as a function of angle so as to generate a diffraction spectrumof the sample. The diffraction spectrum is corrected to compensate for anon-uniform property of the converging beam.

In some embodiments, correcting the diffraction spectrum includesmodifying an angular scale of the diffraction spectrum. Modifying theangular scale may include adjusting the angular scale to compensate foran aberration in the converging beam. Typically, adjusting the angularscale includes calibrating a relation between an angle of the diffractedX-rays and an angular step size in the diffraction spectrum, andapplying the calibrated relation to correct the angular scale of thediffraction spectrum. Further additionally or alternatively, correctingthe diffraction spectrum includes modifying the intensity in thediffraction spectrum. Modifying the intensities may include applying anintensity correction as a function of the angle of the sensed X-rays inorder to compensate for a non-uniform intensity of the converging beam.

In some embodiments, the method includes analyzing the diffractionspectrum so as to identify a characteristic of the sample. In oneembodiment, the sample includes an epitaxial layer that is formed over asubstrate, and the diffraction spectrum includes at least a firstdiffraction peak due to the substrate and a second diffraction peak dueto the epitaxial layer, and analyzing the diffraction spectrum includesapplying the corrected diffraction spectrum in finding an angulardistance between the first and second diffraction peaks.

There is also provided, in accordance with an embodiment of the presentinvention, a method for analysis, which includes directing a convergingbeam of X-rays toward a surface of a sample including an epitaxial layerthat is formed over a substrate. The X-rays that are diffracted from theepitaxial layers and from the substrate are sensed simultaneously whileresolving the sensed X-rays as a function of angle so as to generate adiffraction spectrum including at least a first diffraction peak due tothe substrate and a second diffraction peak due to the epitaxial layer.An angular distance between the first and second diffraction peaks isfound while correcting the diffraction spectrum to account for a depthof penetration of the X-rays into the substrate.

Correcting the diffraction spectrum may include computing a shift of thefirst diffraction peak due to the penetration as a function of angles ofincidence and diffraction of the X-rays.

There is additionally provided, in accordance with an embodiment of thepresent invention, an X-ray detector assembly, including an integratedcircuit, which includes an array of detector elements and a readoutcircuit, adjacent to the array and coupled to read charge out of thedetector elements. A non-metallic shield is positioned over the readoutcircuit so as to prevent X-rays from striking the readout circuit.

In a disclosed embodiment, the shield includes a mono-crystallinematerial, which is oriented so that X-rays diffracted from the shieldare directed away from the readout circuit. Alternatively oradditionally, the shield may include an amorphous material.

There is further provided, in accordance with an embodiment of thepresent invention, apparatus for analysis, including an X-ray source,which is configured to direct a converging beam of X-rays toward asurface of a sample. A detector assembly is configured to sense theX-rays that are diffracted from the sample while resolving the sensedX-rays as a function of angle so as to generate a diffraction spectrumof the sample. A processor is coupled to correct the diffractionspectrum to compensate for a non-uniform property of the convergingbeam.

There is moreover provided, in accordance with an embodiment of thepresent invention, apparatus for analysis, including an X-ray source,which is configured to direct a converging beam of X-rays toward asurface of a sample including an epitaxial layer that is formed over asubstrate. A detector assembly is configured to sense simultaneously theX-rays that are diffracted from the epitaxial layer and from thesubstrate while resolving the sensed X-rays as a function of angle so asto generate a diffraction spectrum including at least a firstdiffraction peak due to the substrate and a second diffraction peak dueto the epitaxial layer. A processor is configured to find an angulardistance between the first and second diffraction peaks while correctingthe diffraction spectrum to account for a depth of penetration of theX-rays into the substrate.

The present invention will be more fully understood from the followingdetailed description of the embodiments thereof, taken together with thedrawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic side view of an X-ray metrology system, inaccordance with an embodiment of the present invention;

FIG. 2A is a schematic, pictorial illustration of an X-ray detector, inaccordance with an embodiment of the present invention;

FIG. 2B is a schematic, sectional view of the X-ray detector of FIG. 2A;

FIG. 3 is a schematic representation of a HRXRD spectrum, in accordancewith an embodiment of the present invention;

FIG. 4 is a schematic, sectional view of elements of an X-ray metrologysystem, illustrating how depth effects are handled in HRXRDmeasurements, in accordance with an embodiment of the present invention;

FIG. 5 is a ray diagram showing parameters used in correcting for deptheffects, in accordance with an embodiment of the present invention;

FIG. 6A is a plot of the angular distribution of X-ray beam intensityemitted by an X-ray source in a metrology system;

FIG. 6B is a plot of a beam uniformity correction function applied inthe metrology system referred to in FIG. 6A, in accordance with anembodiment of the present invention;

FIG. 7 is a ray diagram showing parameters used in compensating forangle shift in HDXRD measurements, in accordance with an embodiment ofthe present invention;

FIG. 8 is a ray diagram showing parameters used in compensating foraberrations in HDXRD measurements, in accordance with an embodiment ofthe present invention;

FIG. 9 is a plot of aberration measured as a function of angle in anX-ray beam used in a metrology system, in accordance with an embodimentof the present invention; and

FIG. 10 is a flow chart that schematically illustrates a method forHRXRD measurement, in accordance with an embodiment of the presentinvention.

DETAILED DESCRIPTION OF EMBODIMENTS Overview

High-resolution X-ray diffraction (HRXRD) can be used to providedetailed information regarding the structure and composition of thinfilm layers, such as epitaxial layers formed on silicon wafers inmanufacturing of semiconductor devices. The technique is describedgenerally in the above-mentioned U.S. patents.

Because of the very small scale and high precision required insemiconductor device production, it is desirable to use a finely-focusedX-ray beam to irradiate the sample under test, and to measure thediffracted X-rays using a tightly-controlled optical system. Even underthese conditions, however, optical and geometrical factors can distortthe measurement results and reduce accuracy. Embodiments of the presentinvention that are described hereinbelow provide methods for estimatingand correcting the diffraction spectrum for a number of these factorsand thus enhancing the accuracy of HRXRD measurements. The correction tothe diffraction spectrum may be in the form of adjustments to theangular and/or intensity scale of the measured spectrum itself, or asadjustments in a model of sample properties that is fitted to themeasured spectrum.

In some embodiments of the present invention, an X-ray source directs aconverging beam of X-rays toward the surface of a sample, such as asemiconductor wafer. A detector array senses the X-rays that arediffracted from the sample while resolving the sensed X-rays as afunction of angle so as to generate a diffraction spectrum of thesample. A processor then corrects the diffraction spectrum to compensatefor non-uniformities of the converging beam.

The corrections applied by the processor may include modifying theangular scale of the diffraction spectrum, particularly to compensatefor aberrations in the converging beam. The angular locations of thepeaks in the diffraction spectrum are a key indicator of the propertiesof the sample, and correction of errors in the angular scale thus has adirect impact on improving the accuracy of measurement of the sampleproperties.

Additionally or alternatively, the processor may modify the intensitiesin the diffraction spectrum in order to compensate for a non-uniformintensity of the converging beam as a function of the angle. Theobserved intensity distribution in the spectrum may also depend on thesize of the test pad from which diffracted X-rays are received, becauseaberrations can cause some of the intensity to fall outside of the pad.This phenomenon can be measured during the setup and characterization ofthe measurement system and then applied during measurements.

Further additionally or alternatively, the processor may correct thediffraction spectrum to account for apparent angular shifts of the peaksin the spectrum that are related to the depth of penetration of theX-rays into the substrate of the sample.

System Description

FIG. 1 is a schematic side view of a system 20 for HRXRD of a sample 22,in accordance with an embodiment of the present invention. Sample 22 maycomprise, for example, a semiconductor wafer with one or more epitaxiallayers formed over the wafer surface. The sample is mounted on a motionstage 24, allowing accurate adjustment of the position and orientationof the sample. An X-ray source 26 directs a converging X-ray beam 28toward a small area 34 on sample 22. Typically, source 26 comprises anX-ray tube 30 with suitable optics 32 to focus and monochromatize beam28. Beam 28 typically subtends at least 2°, and may subtend as much as4° or even more, depending on optics 32, in order to irradiate sample 22over a large range of angles simultaneously.

X-rays are diffracted from sample 22 in a generally diverging beam 38,which is received by a detector assembly 36. The detector assemblytypically comprises a detector array 42, such as a CCD array, comprisingmultiple detector elements, configured so as to resolve beam 38 as afunction of elevation angle θ. Typically, the angular span of array 42is comparable to that of beam 28, i.e., at least 2°, and possibly 4° orgreater. Various types of X-ray sources and detector assemblies may beused in system 20. Details of such components are described, forexample, in the above-mentioned U.S. Pat. Nos. 7,076,024, 7,120,228 and7,551,719.

Beam blockers 39 and 40 (such as a knife edges) and/or other opticalelements may be used to limit beam 28 and/or beam 38 and to blockundesired scattered radiation that might otherwise strike array 42 andinterfere with the diffraction measurement. Another beam blocker 41,oriented perpendicularly to blockers 39 and 40, is used to blockundesired irradiation wavelengths. System 20 may also comprise otherX-ray optical elements (not shown in the figures) for improving beamquality and reducing background radiation, as described, for example, inU.S. patent application Ser. No. 12/683,436, filed Jan. 7, 2010, whosedisclosure is incorporated herein by reference.

The positions of source 26 and detector assembly 36 are controlled bymotion assemblies 44 and 46, respectively. In the simplified view shownin FIG. 1, the motion assemblies comprise curved tracks, which permitthe source and detector assembly to be positioned at the appropriateelevations, typically in the vicinity of the Bragg angles of the layersthat are to be analyzed. Other suitable motion assemblies will beapparent to those skilled in the art. For the sake of this example, itis assumed that the lattice planes creating the diffraction pattern areapproximately parallel to the surface of sample 22, so that theincidence and takeoff angles defined by beams 28 and 38 relative to thesurface are both equal to the Bragg angle. Alternatively, source 26 anddetector assembly 38 may be positioned at different incidence andtakeoff angles in order to measure diffraction from lattice planes thatare not parallel to the surface of sample 22.

In addition, as noted above, stage 24 may be configured to translate theX-Y location on the sample that falls within area 34, as well as torotate the azimuthal angle φ of the sample relative to beam 28. (Asshown in FIG. 1, the X-Y plane is taken to be the sample surface, withthe Z-axis perpendicular to the surface; θ is the elevation anglerelative to the Z-axis; and φ is the azimuthal angle of rotation aboutthe Z-axis.)

A signal processor 48 receives and analyzes the output of assembly 36,so as to measure a spectrum 50 of the flux of X-ray photons diffractedfrom sample 22 as a function of angle at a given energy or over a rangeof energies. Processor 48 may also adjust the positions and operatingparameters of the other components of system 20, including source 26,detector assembly 36, stage 24, and motion assemblies 44 and 46.

Typically, sample 22 has one or more thin surface layers, such as thinfilms, at area 34, so that distribution 50 as a function of elevationangle exhibits a structure that is characteristic of diffraction effectsdue to the surface layer and underlying layers. Processor 48 analyzesthe angular spectrum in order to determine characteristics of one ormore of the layers of the sample, such as the composition, thickness,lattice strain, relaxation, crystalline quality and/or tilt angle of thelayer. For these purposes, the processor may apply methods of analysissuch as those described in the above-mentioned U.S. patents and/or inU.S. patent application Ser. No. 12/958,420, filed Dec. 2, 2010, whosedisclosure is incorporated herein by reference, as well as other methodsthat are known in the art.

As part of this analysis, processor 48 corrects certain inaccuraciesthat may arise in the X-ray measurements due to deviation of thecomponents of system 20 from ideal physical characteristics. Theseinaccuracies may arise, for example, due to non-uniformity andaberrations in the X-ray beam, as well as variations in the depth ofpenetration of X-rays into sample 22. Methods for performing thesecorrections are described in detail hereinbelow.

The components of system 20 and the techniques described herein may beintegrated into systems that provide other types of measurementfunctionality, such as X-ray reflectometry and scattering measurements.Additionally or alternatively, these components and techniques may beintegrated as process monitoring tools in manufacturing systems, such assystems for semiconductor wafer fabrication. Integrated systems of thesetypes are described in greater detail in the above-mentioned patents.

FIGS. 2A and 2B schematically illustrate elements of detector assembly36, showing the use of a shield 54 for blocking background radiation, inaccordance with an embodiment of the present invention. FIG. 2A is apictorial illustration that shows shield 54 and detector array 42 in adevice package 52, while FIG. 2B is a sectional illustration showing therelative positions of the shield and array.

Detector array 42 in this embodiment may be, for example, acharge-coupled device (CCD). In such devices, charge is shifted out ofthe detector elements into a readout circuit comprising a register line56 near the edge of the device, which then outputs a signal indicativeof the charges accumulated (and hence the X-ray intensity sensed) byeach detector element. In conventional CCD designs, the register line isexposed to radiation along with the detector elements, and incidence ofstray electrons on the register line may result in accumulation ofcharge in the register line. The inventors have found that this registerline charge can be a major contributor to the level of background noisein the output signal from array 42.

To reduce this source of noise, register line 56 is covered by shield54, which blocks incident X-rays, as shown in FIG. 2B. Typically, theshield is made from a crystalline material, such as a strip cut from aSi or Ge wafer, which is about 0.7 mm thick and may be mounted about 2mm above the surface of array 42, for instance. The mono-crystallineshield 54 may be oriented so that X-rays diffracted from the shield areangled away from detector array 42. The edge of shield 54 may bepolished, typically to a roughness of about 25 μm, for example, toprevent stray reflections and diffraction at the edge. The use of amono-crystalline shield is superior to metal shields that are used insome applications, since X-rays may diffract from the polycrystallinemetal in many directions, some of which will impinge on the detectorarray. Alternatively, shield 42 may comprise an amorphous material withsufficient X-ray absorbance.

To align shield 54, array 42 may be irradiated with X-rays while theoutput signal from the array is monitored. The shield is slid across thearray until the signal shows that register line 56 and the last few rowsof detector elements adjacent to the register line are blocked. Theshield is then fixed in place. The inventors have found that using amono-crystalline shield in this fashion reduces the background level inthe output signal by about an order of magnitude

FIG. 3 is a schematic representation of a HRXRD spectrum obtained fromsample 22 in system 20, in accordance with an embodiment of the presentinvention. The spectrum is shown on a logarithmic scale in countscaptured by the elements of array 42, as a function of the respectiveelevation angles of the elements. The angular scale in FIG. 3 isadjusted, for the sake of convenience, so that a peak 60 due todiffraction from the silicon wafer substrate is taken as the origin(θ=0). Additional peaks 62 and 64 arise from epitaxial thin-film layersformed over the substrate. The separation between the peaks can be used,for example, to indicate accurately the properties of the layers.

This particular spectrum is shown only by way of example, and system 20may similarly be used to perform HDXRD measurements on samples andlayers of other types, as will be apparent to those skilled in the art.

Techniques for Accuracy Enhancement Correcting for Penetration Depth

FIG. 4 is a schematic, sectional view of elements of system 20,illustrating how depth effects are handled in HDXRD measurements, inaccordance with an embodiment of the present invention. In this example,a thin-film epitaxial layer 70 is formed on the surface of the siliconsubstrate of sample 22. Crystalline structures in the epitaxial layer,as well as the substrate itself, diffract the incident X-ray beam attheir respective Bragg angles (shown in the figure as θ_(sub) for a ray76 incident on the substrate and θ_(film) for a ray 72 incident on athin-film epitaxial layer). The angular displacement between thecorresponding diffracted rays 78 and 74 is indicative of the compositionand lattice conditions of layer 70, as explained above.

As illustrated in FIG. 4, however, the locus of diffraction of theX-rays from layer 70 is above the locus in the substrate of sample 22,leading to an added angular displacement between the respectivediffraction peaks. Diffracted ray 74 is the result of diffraction thattakes place within a few hundred Å of the surface. The origin of ray 78,on the other hand, is effectively at a depth of a few microns, whichresults in a shift of the detected position of the main diffraction peakon detector array 42.

FIG. 5 is a ray diagram showing parameters used in correcting for thisdepth-related shift, in accordance with an embodiment of the presentinvention. To account for the depth effect in measuring the angularseparation between the peaks in the diffraction spectrum, the zero anglein the spectrum (which is normally associated with the substrate peak)is corrected using the parameters shown in the figure. Specifically,referring to FIG. 3, the displacement of peak 60 is calculated based onthe parameters shown in FIG. 5, and processor 48 introduces thecalculated displacement as a correction into the computation of theinter-peak angular separation in order to compensate for the lateraldisplacement effect.

The estimated peak displacement s of the substrate diffraction relativeto the diffraction from layer 70 is given by the formula:

$\begin{matrix}{s \approx {\frac{L_{ext}}{2}\left\lbrack {\frac{1}{\tan \left( {\theta_{B} - \varphi} \right)} + \frac{1}{\tan \left( {\theta_{B} + \varphi} \right)}} \right\rbrack}} & (1)\end{matrix}$

In this formula, L_(ext) is the extinction depth, which can be expressedas twice the penetration depth z_(e), i.e., L_(ext)=2z_(e). Thepenetration depth is defined as the depth in the substrate material atwhich the X-ray beam amplitude is reduced by attenuation by a factor ofe (so that the intensity is reduced by e²) and is given by the formula:

$\begin{matrix}{z_{e} = \frac{\lambda \sqrt{\gamma_{0}{\gamma_{h}}}}{2\pi \sqrt{\chi_{0}\chi_{h}}}} & (2)\end{matrix}$

Here γ₀ and γ_(h) are the direction cosines of the incident anddiffracted beams, and χ₀ and χ_(h) are the electric susceptibilities inthe incident and diffracted directions.

The distance traversed by the X-ray beam through the substrate materialdepends on the Bragg angle θ_(B) and, for non-symmetrical reflections,on the offset angle φ. (For symmetrical reflections, φ=0.) Thepenetration depth depends on these angular factors in a complex way,since the electric susceptibility of the crystalline substrate varieswith the directions of the incident and diffracted beams.

Values of the penetration depth can be computed for various reflectionsand X-ray energies, as described, for example, by Authier in DynamicalTheory of X-ray Diffraction (Oxford, 2005), pages 101-102, which areincorporated herein by reference. Table I below presents these values,along with the corresponding peak displacement values, for a number ofdifferent reflections from Si(001) substrates using Cu Kα X-rays(approximately 8 keV):

Reflection z_(e) (μm) s (μm) 004 1.8 5.2 115 4.0 8.0 224 2.6 9.7

As noted above, processor 48 applies the peak displacement s that islisted in the table (or is otherwise computed for the testing conditionsof relevance) in adjusting the zero-angle position in the XRD spectrumto offset the depth-related shift. In some cases, this zero-angleadjustment is sufficiently small to be neglected in analyzing the XRDspectrum.

Correcting for Beam Non-Uniformity

FIGS. 6A and 6B schematically illustrate a method for calibrating andcorrecting for non-uniformity in the intensity distribution of X-raybeam 28 generated by source 26 in system 20, in accordance with anembodiment of the present invention. FIG. 6A is a plot of the actualangular distribution of the intensity emitted by source 26. Thenon-uniformity of this beam will result in a corresponding intensitymeasurement error in the raw measurements made by detector assembly 36.FIG. 6B is a plot of a beam uniformity correction function applied byprocessor 48 in order to compensate for the non-uniformity of theincident beam and thus correct the error.

To compute the correction function of FIG. 6B, the angular dependence ofthe intensity of beam 28 is measured and calibrated in advance. Detectorarray 42 can be used for this purpose, by shifting detector assembly 36to a position in which it receives beam 28 directly from X-ray source26. In this position, the detector array measures the beam intensity asa function of angle. The output of detector assembly 36 is a vector ofintensities y[j], wherein j is the pixel number. (The detector elementsin the detector array are also referred to as “pixels.”)

To compute the values of the correction function (also referred to asthe “modulator function”), and thus to correct the actual diffractionmeasurements for beam non-uniformity, the elements of the vector y[j]are normalized to be 1 on average. The elements of the modulatorfunction m[j] are calculated according to m[j]=y[j]/Mean(y), whereinMean(y) denotes the mean value of the intensity in some central regionof the angle range, for example from 0.5 to 3.5 degrees. Processor 48then multiplies the intensities in the HRXRD spectrum obtained fromsample 22 by the modulator function values m[i+shift]. The “shift” for agiven measurement is the displacement of the substrate (Si) diffractionpeak of the substrate from its nominal position (not to be confused withthe penetration-related shift value s computed in the precedingsection). The angular shift is calculated using the method described inthe next section. The shift calculation may also take into accountcalibration of the zero-angle that takes place during system setup(which is outside the scope of the present patent application).

The method described above assumes that the area from which diffractedX-rays are received is homogeneous, i.e., the entire area has the samelayer structure. The effective intensity distribution when measuringdiffraction from a small pad can be different, because aberrations cancause some of the irradiating X-rays to fall outside the test pad area,leading to a less uniform effective intensity. Although the presentcorrection procedure is also applicable to small test pads, themodulator function may be adjusted depending on the test pad size.

Compensating for X-Ray Beam Aberrations

Aberrations of X-ray optics 32 may distort beam 28 in both the verticaland horizontal directions. Vertical aberrations (perpendicular to thesurface of the sample) can lead to a displacement between the loci ofdiffraction of substrate diffraction peak 60 and satellite peaks, suchas peak 64, arising from epitaxial layers. The amount of aberration as afunction of ray angle within the beam can be measured by detectingchanges in the X-ray beam incidence location on the sample as a functionof the ray angle. (In the absence of aberration, the location shouldremain constant.) This aberration measurement is then used to model theresulting displacement and its effect on HRXRD measurements, thusgenerating a correction function to be applied by processor 48.

Once the displacement has been calculated, it can be used by processor48 either to adjust the scale of the measured spectrum or to introduce acorrection into a model of layer properties that is fitted to themeasured spectrum. For example, the diffraction angle that is associatedwith each element in detector array 42 can be corrected for aberrationeffects, with the result that the diffraction angle is no longer alinear function of position in the detector array. The processor maythen use an interpolation function, such as cubic spline interpolation,to convert the detector array output back into a linear angular scale.

FIG. 7 is a ray diagram showing parameters used in compensating forangle shift in HDXRD measurements in system 20, in accordance with anembodiment of the present invention. This shift can vary with the angleA at which X-ray source 26 is position to generate incident beam 28, aswell as with the angle B at which detector assembly 36 is positioned inorder to capture diffracted beam 38. Each incoming ray 82, at a relativeangle α in the incident beam, corresponds to an outgoing ray 84, at arelative angle β in the diffracted beam, but the relation between α andβ can vary with A, B and β. It is advantageous that processor 48 have anaccurate value of α in order to correct properly for beam non-uniformity(as explained above) and aberrations (as will be explained below).

The value of α may be calibrated using the relation:

θ_(B)=(A+α)+(B+β)+ε  (3)

wherein ε is an error term that represents all of the systematic errorsin positioning. This error term may be calibrated during measurementsetup and considered to be constant thereafter. To ensure propercalibration, system 20 maintains the sample height at a constant valuerelative to the beam focus, using a laser triangulation displacementgauge, for example. The error term ε may be measured using the followingprocedure:

-   -   1. Perform a source scan of a Si(001) reference sample with        known or small tilt, detecting substrate peak 60 on detector        array 42 while stepping the source axis in fine steps, such as        0.05°. If the reference sample has tilt, then the procedure can        be repeated at two azimuth rotations of the wafer 180° apart,        taking the average of the determined angle values below.    -   2. Fit the substrate peak intensity for all data in the scan,        and plot the fitted peak intensity versus the source-axis angle        A to determine the angle A₀ that corresponds to the ray angle        α=0. (Beyond this angle, the detected peak intensity will drop        rapidly to zero.)    -   3. Note the detector axis position B₀ of the measurement, and        determine the absolute substrate peak position β₀ for the        measurement at the source-axis angle A₀.    -   4. Calculate the error value using the formula:

ε=2θ_(B) −A ₀−(B ₀+β₀)   (4)

This procedure allows ε to be determined to an accuracy of about 0.05°.The estimated value of ε can be checked and refined by applying thecorrections to the source-axis scan data.

Following this calibration, processor 48 can relate the source angle tothe detection angle using the relation α=k−β, wherein k=2θ_(B)−A−B−ε.The angle shift to be applied to the correction data for eachmeasurement is then determined from the absolute detection angle β bythe formula:

shift=β−α=2β−k   (5)

FIG. 8 is a ray diagram showing parameters used in compensating foraberrations in HDXRD measurements, in accordance with an embodiment ofthe present invention. Whereas the calibration computations describedabove assume that all rays in incident beam 26 are focused to a singlepoint on sample 22, in practice aberrations of optics 32 cause someincident rays 90 to deviate from an ideal incident ray 94 at the sameangle A+α. Consequently, a corresponding diffracted ray 92 deviates by acommensurate amount from an ideal diffracted ray 96. The amount ofdeviation of the incident ray is a function of the ray angle, which isexpressed in terms of the aberration a(α). This aberration results in acorresponding displacement of the focal point on the sample:s(α)=a(α)/sin(A+α). This linear displacement is indistinguishable atdetector array 42 from an equivalent angular shift of diffracted ray 92by an amount:

δ(α)=s(α)sin(B+β)/D   (6)

wherein D is the focus-detector distance.

FIG. 9 is a plot of aberration-related shift s(α), measured as afunction of angle in beam 28 emitted by X-ray source 26, in accordancewith an embodiment of the present invention. The aberration measurementscan be made in a similar fashion to the measurement of angle deviationdescribed above, by performing a source scan and detecting changes inthe position of a strong diffraction peak, such as substrate peak 60,after removing any displacement due to the surface of the sample notbeing exactly on the center of rotation of the source axis.Alternatively, other methods that are known in the art may be used tomeasure the aberrations. The plot in the figure shows the aberration interms of the deviation of the measured location of the X-ray beam focus,as a function of the angle of incidence of the X-rays, relative to theideal location. Over the central part of the scan shown in the figure,the deviation among the pixels is on the order of several microns.

The deviation of the focal location due to aberrations can be treated asa variation in the angular step size from pixel to pixel. In otherwords, the angular increment from pixel to pixel is not constant, butrather varies across detector array 42 by an amount related to the localaberration. To correct HRXRD measurements in system 20 for theseaberration effects, processor 48 may compute and apply a correctionfactor in translating the pixel index into diffraction angle, giving thecorrected angular position α_(j) corresponding to each pixel j:

α_(j) =jΔα−δ(α_(j))   (7)

Here Δα=p/D is the angular pixel size (wherein p is the pitch of thedetector elements). The correction factor δ is computed based on thecalibration data, as defined by equation (6).

System Operation

FIG. 10 is a flow chart that schematically illustrates a method forHRXRD measurement, in accordance with an embodiment of the presentinvention. The method is described hereinbelow, for the sake ofconvenience and clarity, with specific reference to the components ofsystem 20. The principles of this method, however, may similarly beapplied, mutatis mutandis, in other X-ray measurement systems andapplications.

The method includes a calibration stage (steps 100-104), followed by asample testing stage (steps 106-114), in which the calibration resultsare applied. The calibration stage starts with an angle calibration step100, in which the elements of system 20 are operated to measure theangular errors in the system and the relationship between detector andsource angles, as described above with reference to FIG. 7. Thisrelationship is used to determine the angular shift of both theuniformity and aberration corrections that are applied in the sampletesting stage.

The elements of system 20 are then operated to measure the degree ofnon-uniformity of beam 28 generated by source 26, at a non-uniformitycalibration step 102. This measurement is applied in modeling the beamintensity variation with angle, so as to derive a correction function,as described above with reference to FIGS. 6A and 6B.

Additionally, the elements of system 20 are operated to measure spatialdeviations of the beam from the ideal focus position as a function ofangle, in an aberration calibration step 104. This measurement is usedto derive an aberrations correction function, as described above withreference to FIGS. 8 and 9.

To begin the testing stage, a measurement location is chosen on sample22, and stage 24 is operated to bring this location into the focus ofbeam 28 at the desired angle, at a location selection step 106. Source26 and detector assembly 36 may then be adjusted to optimize the beamquality for the angle and location in question, at a setup optimizationstep 108. This step may be carried out manually, under direct control ofan operator of system 20, or automatically, under control of processor48. The “optimal” beam parameters in this context are those thatminimize the non-uniformity and aberrations of the beam that is incidenton the sample.

To adjust the source and detector locations, processor 48 may identifysubstrate peak 60 in the spectrum output by detector assembly 36. Theprocessor may then operate motion assemblies 44 and 46 to move source 26and detector assembly 36 so that peak 60 appears at a certain selectedangular position. As some of the calibration and corrections functionsdescribed above are dependent on the source and detector angles A and B,processor 48 uses the adjusted source and detector angles to select theappropriate values of the calibration factors to be used subsequently.

Next, processor 48 actuates system 20 to capture HRXRD data from theselected location on sample 22, at a data capture step 110. Theprocessor then corrects the spectral data for the deviations andnon-uniformities described above, at a correction step 112. Thesecorrections typically include variations in penetration depth (FIGS.4-5), and beam non-uniformity (FIGS. 6A-6B), aberrations (FIGS. 8-9).Having performed the necessary corrections, processor 48 outputscorrected spectral data. The processor may apply these data in computingproperties of sample 22, and particularly of thin film layers on thesample, at a property computation step 114.

Although the method of FIG. 10 involves a certain specific combinationof corrections that are appropriate to system 20, it is not alwaysnecessary that all of these corrections be applied to HRXRD data. Forexample, it may in some circumstances be possible to omit certaincorrections if they do not contribute significantly to the accuracy of agiven measurement, and thus to perform only one or a few of the types ofcorrections that are described above. Alternatively, in othercircumstances, it may be desirable to combine one or more of the abovetypes of corrections with other calibration and data correctiontechniques that are known in the art.

It will thus be appreciated that the embodiments described above arecited by way of example, and that the present invention is not limitedto what has been particularly shown and described hereinabove. Rather,the scope of the present invention includes both combinations andsubcombinations of the various features described hereinabove, as wellas variations and modifications thereof which would occur to personsskilled in the art upon reading the foregoing description and which arenot disclosed in the prior art.

1. A method for analysis, comprising: directing a converging beam ofX-rays toward a surface of a sample; sensing the X-rays that arediffracted from the sample while resolving the sensed X-rays as afunction of angle so as to generate a diffraction spectrum of thesample; and correcting the diffraction spectrum to compensate for anon-uniform property of the converging beam.
 2. The method according toclaim 1, wherein correcting the diffraction spectrum comprises modifyingan angular scale of the diffraction spectrum.
 3. The method according toclaim 2, wherein modifying the angular scale comprises adjusting theangular scale to compensate for an aberration in the converging beam. 4.The method according to claim 3, wherein adjusting the angular scalecomprises calibrating a relation between an angle of the diffractedX-rays and an angular step size in the diffraction spectrum, andapplying the calibrated relation to correct the angular scale of thediffraction spectrum.
 5. The method according to claim 1, whereincorrecting the diffraction spectrum comprises modifying intensities inthe diffraction spectrum.
 6. The method according to claim 5, whereinmodifying the intensities comprises applying an intensity correction asa function of the angle of the sensed X-rays in order to compensate fora non-uniform intensity of the converging beam.
 7. The method accordingto claim 1, and comprising analyzing the diffraction spectrum so as toidentify a characteristic of the sample.
 8. The method according toclaim 7, wherein the sample includes an epitaxial layer that is formedover a substrate, and wherein the diffraction spectrum comprises atleast a first diffraction peak due to the substrate and a seconddiffraction peak due to the epitaxial layer, and wherein analyzing thediffraction spectrum comprises applying the corrected diffractionspectrum in finding an angular distance between the first and seconddiffraction peaks.
 9. The method according to claim 8, wherein applyingthe corrected diffraction spectrum comprises correcting the diffractionspectrum to account for a depth of penetration of the X-rays into thesubstrate.
 10. The method according to claim 1, wherein sensing theX-rays comprises receiving the detecting the X-rays using an integratedcircuit comprising a detector array and a readout circuit, wherein thereadout circuit is covered by a non-metallic shield to prevent thediffracted X-rays from striking the readout circuit.
 11. A method foranalysis, comprising: directing a converging beam of X-rays toward asurface of a sample including an epitaxial layer that is formed over asubstrate; simultaneously sensing the X-rays that are diffracted fromthe epitaxial layers and from the substrate while resolving the sensedX-rays as a function of angle so as to generate a diffraction spectrumcomprising at least a first diffraction peak due to the substrate and asecond diffraction peak due to the epitaxial layer; and finding anangular distance between the first and second diffraction peaks whilecorrecting the diffraction spectrum to account for a depth ofpenetration of the X-rays into the substrate.
 12. The method accordingto claim 11, wherein correcting the diffraction spectrum comprisescomputing a shift of the first diffraction peak due to the penetrationas a function of angles of incidence and diffraction of the X-rays. 13.An X-ray detector assembly, comprising: an integrated circuit comprisingan array of detector elements and a readout circuit, adjacent to thearray and coupled to read charge out of the detector elements; and anon-metallic shield positioned over the readout circuit so as to preventX-rays from striking the readout circuit.
 14. The assembly according toclaim 13, wherein the shield comprises a mono-crystalline material,which is oriented so that X-rays diffracted from the shield are directedaway from the readout circuit.
 15. The assembly according to claim 13,wherein the shield comprises an amorphous material.
 16. Apparatus foranalysis, comprising: an X-ray source, which is configured to direct aconverging beam of X-rays toward a surface of a sample; a detectorassembly, which is configured to sense the X-rays that are diffractedfrom the sample while resolving the sensed X-rays as a function of angleso as to generate a diffraction spectrum of the sample; and a processor,which is coupled to correct the diffraction spectrum to compensate for anon-uniform property of the converging beam.
 17. The apparatus accordingto claim 16, wherein the processor is configured to correct thediffraction spectrum by modifying an angular scale of the diffractionspectrum.
 18. The apparatus according to claim 17, wherein the processoris configured to adjust the angular scale to compensate for anaberration in the converging beam.
 19. The apparatus according to claim17, wherein the processor is configured to calibrate a relation betweenan angle of the diffracted X-rays and an angular step size in thediffraction spectrum, and to apply the calibrated relation to correctthe angular scale of the diffraction spectrum.
 20. The apparatusaccording to claim 16, wherein the processor is configured to correctthe diffraction spectrum by modifying an intensity in the diffractionspectrum.
 21. The apparatus according to claim 20, wherein the processoris configured to apply an intensity correction as a function of theangle of the sensed X-rays in order to compensate for a non-uniformintensity of the converging beam.
 22. The apparatus according to claim16, and wherein the processor is configured to analyze the diffractionspectrum so as to identify a characteristic of the sample.
 23. Theapparatus according to claim 22, wherein the sample includes anepitaxial layer that is formed over a substrate, and wherein thediffraction spectrum comprises at least a first diffraction peak due tothe substrate and a second diffraction peak due to the epitaxial layer,and wherein the processor is configured to use the corrected diffractionspectrum in finding an angular distance between the first and seconddiffraction peaks.
 24. The apparatus according to claim 23, wherein theprocessor is configured to correct the diffraction spectrum to accountfor a depth of penetration of the X-rays into the substrate.
 25. Theapparatus according to claim 16, wherein the X-ray source comprises anintegrated circuit comprising a detector array and an readout circuit,wherein the readout circuit is covered by a non-metallic shield toprevent the diffracted X-rays from striking the readout circuit. 26.Apparatus for analysis, comprising: an X-ray source, which is configuredto direct a converging beam of X-rays toward a surface of a sampleincluding an epitaxial layer that is formed over a substrate; a detectorassembly, which is configured to sense simultaneously the X-rays thatare diffracted from the epitaxial layer and from the substrate whileresolving the sensed X-rays as a function of angle so as to generate adiffraction spectrum comprising at least a first diffraction peak due tothe substrate and a second diffraction peak due to the epitaxial layer;and a processor, which is configured to find an angular distance betweenthe first and second diffraction peaks while correcting the diffractionspectrum to account for a depth of penetration of the X-rays into thesubstrate.
 27. The apparatus according to claim 26, wherein theprocessor is configured to correct the diffraction spectrum by computinga shift of the first diffraction peak due to the penetration as afunction of angles of incidence and diffraction of the X-rays.